Eastern Polynesian astronomy was practiced by navigators and astronomer-priests who were in charge of adjusting the lunar calendar and their annual ritual cycle of activities known as ‘The Work of the Gods’. The festivity known in Polynesia as Matariki, Matali'i or Matari'i was related to the heliacal and acronical rising and setting of the Pleiades. A study of 75 marae on the island of Raivavae, Austral Islands and of 7 marae in the island of Raiatea, Society Islands shows that there are alignments towards important star positions associated with this ritual cycle. Their use as observatories has not been documented and therefore these alignments could have served solely ritual purposes. On Easter Island all information regarding the Matariki festival coincides with the arrival of a Spanish expedition in 1770.

Over the past five years, the Egyptian-Spanish Mission on the archaeoastronomy of ancient Egypt and its collaborators has been performing an ambitious scientific project with the aim of studying the cosmovision of the ancient civilization of the pharaohs. Part of the project has consisted of a re-analysis of the iconographic and historical sources that has allowed, among other things, a reassessment of the calendar theory and a new proposal for the sky-maps of ancient Egypt. For various reasons, Archaeoastronomy has not been one of the favourite disciplines of egyptologists in the past. Probably because of this, important questions such as the orientation of Egyptian temples and the relevance of astronomy in this respect had never been afforded with the requisite seriousness and depth. Our work has had among its various priorities, the solution of this problem. In order to achieve this, our team has so far measured the orientation of some 330 temples in the Valley, the Delta, the Oases and the Sinai. The aim is to find a correct and almost definitive answer to the question of whether the ancient Egyptian sacred constructions were astronomically aligned or not. Our results may provide an affirmative answer.

Let n points in the plane be generated by some specified random mechanism and suppose that N(∊) of the resulting triads form triangles with largest angle ≧ π – ∊. The main object of the paper is to obtain asymptotic formulae for and Var (N(∊)) when ∊ ↓ 0, and to solve the associated data-analytic problem of testing whether an empirical set of n points should be considered to contain too many such ∊-blunt triads in the situation where the generating mechanism is unknown and where all that can be said about the tolerance ∊ is that it must be allowed to take values anywhere in a given interval (T0, T1) (0 < T0 < T1). This problem is solved by the introduction of a plot to be called the pontogram and by the introduction of simulation-based significance tests constructed by random lateral perturbations of the data.